Re: Thread::tdlen: Objects of unequal length

*To*: mathgroup at smc.vnet.net*Subject*: [mg121925] Re: Thread::tdlen: Objects of unequal length*From*: Leonid Shifrin <lshifr at gmail.com>*Date*: Thu, 6 Oct 2011 04:26:51 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201110050804.EAA07154@smc.vnet.net>

You shouldn't have used the normal multiplication operator (*) for matrix multiplication, because it assumes element-wise multiplication for lists (and therefore matrices, and generally tensors). A bit more technically, this is due to Times (*) having Listable attribute. In some other systems, the multiplication operator for matrices defaults to matrix multiplication, while element-wise multiplication is a separate operator. Not so in Mathematica, where matrices are not particularly central to the system's design. In Mathematica, there is a special-purpose command Dot (.) designed for matrix multiplication. So, s = {x1, x2, x3, x4} t = {{0.0284435, 0.00395759, 0.000211963, 0.0357403}, {0.00395759, 0.0113862, -0.000199939, -0.000556137}, {0.000211963, -0.000199939, 0.00118147, -0.00043913}, {0.0357403, -0.000556137, -0.00043913, 0.0649449}} In[10]:= s.t.s Out[10]= x2 (0.00395759 x1+0.0113862 x2-0.000199939 x3-0.000556137 x4)+x3 (0.000211963 x1-0.000199939 x2+0.00118147 x3-0.00043913 x4)+x1 (0.0284435 x1+0.00395759 x2+0.000211963 x3+0.0357403 x4)+(0.0357403 x1-0.000556137 x2-0.00043913 x3+0.0649449 x4) x4 You don't need double-list braces for your vector, and neither do you need to Transpose it. Cheers, Leonid On Wed, Oct 5, 2011 at 12:04 PM, SysInv <johan at systeminvestors.se> wrote: > This problem is driving me crazy. I'm trying to multiply matrices, where > one is 1x4 (s) and the other is 4x4 (t) and the multiplication is > s*t*Transpose[s] > > Despite this I get the error message that the objects is of unequal length. > The matrices are: > > s={{x1,x2,x3,x4}} > > > t={0.0284435,0.00395759,0.000211963,0.0357403},{0.00395759,0.0113862,-0.000199939,-0.000556137},{0.000211963,-0.000199939,0.00118147,-0.00043913},{ > 0.0357403,-0.000556137,-0.00043913,0.0649449} > > I must use double level in the 1 row matrix, since otherwise Transpose[] > complains that it needs at least 2 levels. I tried without this as well, but > I keep getting: > > Thread::tdlen : Objects of unequal length in > {{x1,x2,x3,x4}}{{0.0284435,0.00395759,0.000211963,0.0357403},<<2>>,{<<10>>,<<3>>}}{{x1},{x2},{x3},{x4}} > cannot be combined. >> > > . when I run s*t*Transpose[s]. > > I've spent hours trying to figure this simple problem out, but without any > luck. Any pointers guys? It doesn't help if I change the order of the > transpose... >

**References**:**Thread::tdlen: Objects of unequal length***From:*SysInv <johan@systeminvestors.se>